Moon’s Motion: Lunar Month

Synodic month: time from one new moon to the next (29.53 days)

Sideral month: time it takes the Moon to complete one orbit (27.32 days)

Solar Eclipse: Path of the Umbra and Penumbra

1999 - total solar eclipse NASA - GSFC

Motions of the Planets. Geocentric and Heliocentric Motions of the Planets. Geocentric and Heliocentric SystemsSystems

- Planets reflect light; they do not emit light like stars because they lack the central engine of a star: the thermonuclear burning in the core.

- Unlike stars, they do not twinkle, because planets have a sizable disk, while stars are point sources.

- Planets visible by eye and known to the ancient astronomers: Mercury, Venus, Mars, Jupiter and Saturn

Planets: basic information

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Mars Retrograde Motion: January 2, 1995 - March 24, 1995

WestEast

Richard Pogge - Ohio State University

- The speed at which the Sun and Moon travel around the celestial sphere is nearly constant. However, the planets do not travel at constant speed along the ecliptic.

Motions of the Planets: Characteristics

- Like the Sun and Moon all planets rise in the east and set in the west once a day (diurnal motion due to Earths’ rotation about its axis).

- With respect to the fixed stars, the Sun and Moon move from west to east along the ecliptic path. This is called direct motion. The planets too move along the ecliptic path. However, each of the planets, besides the direct motion, moves in the opposite sense, that is they have a retrograde motion.

Mars and Uranus: APOD Dec 16, 2003 - Tunc TezelMars and Uranus: APOD Dec 16, 2003 - Tunc Tezel

The Solar System: Planets are approximately in the same plane

Ptolemy’s system (geocentric) system: 13-volume work “Almagest”

Ptolemy’s system predicted positions of the Sun, Moon and planets accurately; it was used for ~1000 years as a fundamental work. For the calculations, he used records of planet positions for hundreds of years. There were used some 80 epicycles, including elliptical ones. The system was very complex with no physical explanation.

87 - 150 A.D.

Explaining the Retrograde Motion: the Geocentric Model

The Copernican (Heliocentric) System

Nicolaus Copernicus (1473-1543); “De Revolutionibus”

NASA - JPL animation

Planetary Orbits and Configurations: Copernicus’s system

Inferior planets - Mercury and Venus;

- they are visible near the Sun -> therefore their orbits are smaller than Earth’s orbit

Superior planets - Mars, Jupiter, Saturn, Uranus, Neptune

- sometimes they are visible on the celestial sphere, opposite the Sun, high above horizon at midnight -> therefore their orbits are larger than Earth’s orbit

Planetary Orbits and Configurations

Inferior planet

Planetary Orbits and Configurations

Superior planet

Orbital Periods

Synodic period: time between two successive identical configurations as seen from the Earth; can be determined from observations

Sideral period: true orbital period of a planet (time it takes a planet to complete one full orbit around the Sun); can be determined from calculations

Copernicus calculated the sidereal periods of planets, and their relative distances from the Sun, and found a relationship between these two quantities.

Inferior planet: 1/P = 1/E + 1/SInferior planet: 1/P = 1/E + 1/S

Superior planet: 1/P = 1/E - 1/SSuperior planet: 1/P = 1/E - 1/S

P = sidereal period of the planet

E = sidereal period of the Earth

S = synodic period of the planet

Copernican System

1) Explained the retrograde motions of planets

2) Explained the visibility of planets in the sky in light of their position with respect to the Sun

3) Predicted positions of planets, but because he used circular orbits, the predictions were not that accurate; he had to introduce epicycles to account for the true elliptical orbits

4) Found a relationship between orbital period and distance from the Sun, that all planets obey.

Tycho Brahe (1546-1601): The Observer

Uraniborg, “heavenly castle”

Stjenborg, “star castle”

No telescopes!

Accuracy of positions = 1’

Tycho Brahe was against the Copernican system; his argument was that if the Earth is moving, then nearby stars should appear to shift their positions with respect to background stars: parallax effect

www.globalserve.net

Tycho’s Supernova

- November 11, 1572 - a bright star appeared in the constellation of Cassiopeia; it was brighter than Venus! Tycho’s careful observations revealed no parallax for this new object. But this work made him well known and attracted financial support for his observatory.

Tycho’s supernova in X-ray ROSAT

To Kepler

Tycho Brahe measured positions of ~800 stars and the positions of the Moon, Sun for 20 years, almost daily. His measurements of stars’ positions detected no parallax effect, because stars are too far away for his measurement precision.

Finally, he moved to Prague, where he hired mathematicians and astronomers, including Johannes Kepler.

Johannes Kepler (1571-1630): The Mathematician

Key idea: planets revolve around the Sun in elliptical orbits

Kepler was able to match precisely Tycho’s observations

Kepler’s Laws: 1 and 2

Kepler’s Laws: 3

Kepler’s Laws

1) The orbit of a planet around the Sun is an ellipse, with the Sun at one focus.

2) Law of equal areas: a line joining a planet and the Sun sweeps out equal areas in equal interval of times.

3) The square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of the orbit.

P2 = a3 (P - sidereal period in years, a - semimajor axis in AU)

The laws predicted the motions of planets with better accuracy than any The laws predicted the motions of planets with better accuracy than any geocentric model.geocentric model.

He did not prove that the planets orbit the Sun.He did not prove that the planets orbit the Sun.

He was not able to explain why planets move in accordance with his He was not able to explain why planets move in accordance with his three laws.three laws.